A NUMERICAL FRAMEWORK FOR MODELING FLUID FLOW THROUGH FRACTURED POROUS MEDIA

Groundwater flow in fractured aquifers embraces the Darcian and laminar flux in the rock matrix, the laminar flux in the fractures and the turbulent flow in the conduits or macro-fractures. Any physics-based model that aims to reproduce the whole phenomenon should consider parameters ranging from the hydraulic conductivity in the rock matrix to the coefficients that model the turbulent flow in the conduits. Besides, the scale of the domain studied should be large enough to include the length scale of the controlling heterogeneities and small enough to capture the variations that take place in the hydrogeological parameters. This complexity leads to numerical models that either discretize each heterogeneity or average the material parameters associated with them. The first approach results in computationally expensive numerical schemes, and can only model small domains, while the second approach averages vastly different velocities, resulting in a loss of accuracy of the solution.

In this work we present a numerical model that reproduces the exact geometry of the fractures but uses coarse meshes for the matrix rock. The model allows an analysis of large domains at reasonable computational costs. We consider Darcian flux in both the rock matrix and fractures. The formulation is applicable to cases where the fractures have been refilled with sediments, or to stratified geologic media composed of layers with thicknesses that are much smaller than the size of the domain. The formulation considers different storage capacities and hydraulic permeabilities on each domain and reproduces the mass exchange that occurs when the fluid pressure in the cracks is different compared with the surrounding points in the rock matrix.

The numerical framework uses a vertex-centered finite volume scheme along with a homogenization procedure performed for the elements crossed by a crack. The mass exchange terms are defined with the aid of an analytical solution provided by the equivalent problem of fluid conduction within a layered medium having different hydraulic conductivities. The method is locally conservative and suited to unstructured grids, and can accurately resolve the single-phase coupled fluid flow on both the rock matrix and the fractures.